Optimizing vendor selection in food supply chains: a goal programming approach using interval type-2 trapezoidal fuzzy numbers

The selection of an effective and efficient vendor plays a crucial role in achieving a competitive advantage in food supply chain management. This study focuses on the complex decision-making process of vendor selection problem, considering multiple quantitative and qualitative factors. The primary objectives of this research are to minimize net ordering costs, transportation costs, and late deliveries. Recognizing the presence of uncertainty in input parameters, Interval type-2 trapezoidal fuzzy numbers are used to effectively capture and represent this uncertainty. Through the calculation of expected values, a precise equivalent form is derived. The study employed exponential smoothing forecasting analysis to estimate product demand accurately, reducing the risk of shortages and associated financial losses. To attain a mutually satisfactory solution, a fuzzy goal programming methodology was applied. A numerical example was presented to illustrate the methodology's practical applicability and provide deeper insights into its underlying concepts. The solution successfully minimized the net ordering cost for aggregate demand to a value of 6,115,073. The total net cost of transportation for all products was reduced to 279,361, and the number of vendors' late deliveries was minimized to 153,152. The order quantities for the selected vendors were determined as 5236, 9376, 6358, and 4360 units, respectively. Vendors 1, 3, and 4 exhibited superior performance, whereas Vendor 2 experienced a substantial reduction in allocation due to poor performance.